1. Technical Field
This invention pertains to devices and methods for collecting electromagnetic radiation and converting such electromagnetic radiation to electrical energy. In particular, the invention relates to devices and methods for converting solar radiation to electrical energy.
2. Description of Related Art
Phyllotaxis is the ordered arrangement of branches and leaves on a plant. The basic patterns are alternate, opposite, whorled, or spiral. With an alternate pattern, branches or leaves switch from side to side. An alternate distichous phyllotaxis means that each branch or leaf growing at a single node is disposed in a single rank along the branch (such as in grasses). In an opposite pattern, two branches or leaves grow in opposite directions from the same node. In an opposite pattern, if successive branch or leaf pairs are perpendicular, this is called decussate. A whorled pattern consists of three or more leaves at each node. An opposite branch or leaf pair can be thought of as a whorl of two branches or leaves. A whorl can occur as a basal structure in which all of the leaves or branches are attached at the base of a shoot or stem, and the internodes are small or nonexistent. A basal whorl with a large number of branches or leaves spread out in a circle is called a rosette. A multijugate pattern is a spiral composed of whorls.
A repeating spiral branch or leaf arrangement can be represented by a fraction or ratio describing the sequence of windings branch-by-branch and/or leaf-by-leaf. The ratio is expressed with the denominator being the number of branches or leaves emanating from a stem or branch, and the numerator being the number of spiral rotations around the stem or branch over which those leaves or branches are distributed.
It has been observed that the numerator and denominator often consist of a Fibonacci number and its second successor, respectively. In general, a Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. If the Fibonacci sequence is denoted F(n), where n is the first term in the sequence, the following equation obtains for n=0, where the first two terms are defined as 0 and 1 by convention:F(0)=0, 1, 1, 2, 3, 5, 8, 13, 21, 34 . . .
In some cases, it is customary to use n=1 as a first term, such that the first two terms are defined as 1 and 1 by default, and therefore:F(1)=1, 1, 2, 3, 5, 8, 13, 21, 34 . . .
Mathematically, the Fibonacci sequence is expressed by the formula:F(1)=1F(2)=1F(n)=F(n−1)+F(n−2)
The Fibonacci sequence appears as a mathematical pattern in many phenomena in nature, including the phyllotaxic architecture in trees and plants. Deciduous trees such as the oak, elm, cherry, and beech species have unique phyllotaxic patterns in their branches and leaves that generally correspond to the Fibonacci sequence. As described previously, the repeating spiral pattern of branches in each species can be represented by a fraction describing the angle of anti-clockwise windings branch-by-branch and/or leaf-by-leaf, with the numerator and denominator consisting of a Fibonacci number and its second successor.
For example, starting at a branch on the main trunk in the oak species, the general phyllotaxic architecture pattern of branches is observed to be five (5) branches distributed over a spiral of two rotations around the trunk. At two rotations, the next branch is positioned vertically and directly above the starting point, and the 2/5 rotation/branch pattern repeats. Thus, the Fibonacci pattern is mathematically expressed as 2/5. Other species of trees are also observed to have unique Fibonacci architecture. In the elm species, alternate branches or leaves will have a Fibonacci pattern of 1/2, i.e., one rotation has two leaves/branches. In beech and hazel, the Fibonacci architecture is 1/3, one rotation having three leaves/branches. In poplar and pear trees, the ratio is 3/8, and in willow and almond the ratio is 5/13. TABLE 1 provides a summary of the observed spiral windings in the phyllotaxic architecture of these common trees.
TABLE 1Fibonacci architecture of branchesand leaves in some common trees.TREE SPECIESBRANCHESTURNSOak52Elm21Cherry32Beech31Poplar52Weeping willow83Pear83Almond138
The number of branches or leaves is sometimes called rank, in the case of simple Fibonacci ratios, because the leaves or branches line up in vertical rows. It is believed that phyllotaxic architecture improves the efficiency of photosynthesis in trees and plants.
A photovoltaic (“PV”) array is a linked collection of photovoltaic modules, which are in turn made of multiple interconnected solar cells. The cells convert solar energy into direct current electricity via the photovoltaic effect. The power that one module can produce is seldom enough to meet requirements of a home or a business, so a plurality of modules are linked together to form an array. Most PV arrays use an inverter to convert the DC power produced by the modules into alternating current that can connect to the existing infrastructure to power lights, motors, and other loads. The modules in a PV array are usually first connected in series to obtain the desired voltage; the individual strings are then connected in parallel to allow the system to produce more current.
At high noon on a cloudless day at the equator, the power of the sun is about 1 kW/m2, on the Earth's surface, to a plane that is perpendicular to the sun's rays. Mechanized tracking devices are a common technique utilized to assist PV arrays to track the sun through each day to greatly enhance energy collection. However, tracking devices add cost and require maintenance, so it is more common for PV arrays to have fixed mounts that tilt the array and face due South in the Northern Hemisphere. (Alternatively in the Southern Hemisphere, arrays face due North). The tilt angle can be varied for the season, but if fixed, should be set to give optimal array output during the peak electrical demand portion of a typical year. Fixed positioning, even under optimal conditions, however, has inherent limitations that can compromise the production of electricity. In extreme northern and southern latitudes, the declination and latitude of the sun during winter months can greatly reduce the efficiency of a conventional PV array.
Other factors adversely affect PV array performance. The electrical output of photovoltaic cells is extremely sensitive to shading. When a portion of a PV array is shaded, the output falls dramatically due to electrons reversing course through the shaded portion of the p-n junction. Therefore, it is extremely important that a conventional PV array is not shaded by trees, architectural features, flag poles, or other obstructions. PV array efficiency can also be adversely affected by atmospheric and organic factors. Sunlight can be absorbed by dust, fallout, precipitation or other impurities at the surface of a module. This can cut down the amount of light that actually strikes the cells by as much as half. Maintaining a clean module surface will increase output performance over the life of the module. Module output and life are also degraded by increased temperature. By allowing ambient air to flow over PV modules, and if possible, behind them, this problem is reduced. Conventional PV array designs do not normally allow or compensate for these adverse factors, thereby diminishing the power efficiency of the PV array.
In view of the multitude of factors that adversely affect the overall efficiency and economics of solar energy conversion, there remains a need for solar arrays with improved efficiency in collecting and converting solar energy to useable electrical energy.